Algebras, Coalgebras, Monads and Comonads

Algebras, Coalgebras, Monads and Comonads (2001)

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by Neil Ghani , Christoph Lüth , Federico De Marchi , John Power

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Datum	Value	Source
TITLE	Algebras, Coalgebras, Monads and Comonads	user correction - Legacy Corrections
AUTHOR NAME	Neil Ghani	user correction - Legacy Corrections
AUTHOR NAME	Christoph Lüth	user correction - Legacy Corrections
AUTHOR NAME	Federico De Marchi	user correction - Legacy Corrections
AUTHOR NAME	John Power	user correction - Legacy Corrections
AUTHOR AFFIL	a; Department of Mathematics and Computer Science, University of Leicester; b; FB 3 \| Mathematik und Informatik, Universitat Bremen; c; Laboratory for Foundations of Computer Science, University of Edinburgh	user correction - Legacy Corrections
ABSTRACT	Whilst the relationship between initial algebras and monads is well-understood, the relationship between nal coalgebras and comonads is less well explored. This paper shows that the problem is more subtle and that final coalgebras can just as easily form monads as comonads and dually, that initial algebras form both monads and comonads. In developing these theories we strive to provide them with an associated notion of syntax. In the case of initial algebras and monads this corresponds to the standard notion of algebraic theories consisting of signatures and equations: models of such algebraic theories are precisely the algebras of the representing monad. We attempt to emulate this result for the coalgebraic case by defining a notion cosignature and coequation and then proving the models of this syntax are precisely the coalgebras of the representing comonad.	user correction - Legacy Corrections
YEAR	2001	user correction - Legacy Corrections
CITATIONS	24 found	ParsCit 1.0